Math
There is no doubt in my mind that without mathematics, civilization as we know it would be in the toilet! But, there is a lot of life forms that have lived for thousands, if not millions of years without the benefit of mathematics. You can write down, and download all the mathematics in the world on a storage disk, and put it in your pocket; but do you have a pocket full of mathematics, or do you have a disk with physical or magnetic squiggles on it, in your pocket? What is the physical real thing in your pocket? Does one plus one add up by itself? Does mathematics have life without mind, or machine of man. Can it power itself to do work without man? I am sorry, but mathematics is not something I can fill my grocery cart with, and return home to eat. It is not an entity of the real Universe. It was found in our minds, not behind a rock, or in a hole in the ground. The Universe would continue pretty much on its own without mathematics. The natural real physical Universe functions without it.
In the Universe prior to man on Earth... there were atoms, and sub-atomic particles. There were rain drops. There were things that were singular and multiple grouping. Some things were large and some small. There was many things that could be sorted, measured, arranged, cataloged, and etc. Did all this stuff require mathematics to come into reality? Does and did the Universe require a mathematical organization, plan, or formulation? Was it all accidental cohesion, or adhesion leading to organization emerging from a random primordial pot of electromagnetic goop? Or, was the Universe created with some mathematical organization by the hands of a divine entity? The probability of learning the answers for these type of questions anytime soon is extremely slim or none! I surely cannot answer these questions. No matter what your belief... the formulae for the Universe appears not to be written on any scrolls. If you believe accidental or intentional or somewhere in-between... it is just your belief in your mind, which is imagination, maybe true or maybe false, but remains unsubstantiated. I must go with the real probability of the existence of the Universe before mankind, and before the mathematics of man; but not go into any mathematics of creation. Thus I must herein classify mathematics as fantasy.
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On the very lowest rung of mathematics we probably would find zero. Zero signifying the absence of something. It could signify a nothingness of the highest degree, as infinite nothing... but that is a fantasy of the mind. Usually it is the absence of something one, or more. Next, we have one, or a single something. Then we move to two and etc. But, two is never exactly like one. Even if in your mind you imagine a two, identical to one... it has a different name... two, thus required to give it identity, and it exists separately in a different location than one. For two to be identical, and exactly like one, it would have to be, as one; in all respects, as name, location, as well as likeness. The point is, there is nothing exactly like another entity. This means that when you have 12 oranges... or 12 of anything... they may be oranges, but they are not exactly all the same. Identical 12 of anything can only exist in our minds.
In Geometry a point is one of the initial concepts. It is like a dot, or tiny speck imagined in a location in three dimensional space. I say imagined, because it has no dimensions of size, except a pseudo measurable position of location. I have found, when measuring to a point of nothing... it is very very easy to be little bit to the right or left, and or up or down!? Next, for Geometry is the straight line. In general it is a straight row of infinite points, of nothing, from one point of nothing location, to another point of nothing location. Again, we can imagine this... but if you also imagine making a row of any length of points with no width, height, or depth... it is extremely hard to create the line. But__ we can and do indeed imagine lines, points, circles, triangles, and such! I love geometry and trigonometry. But, points, lines, numbers, and etc., are only in our minds. Getting imaginary fantasy mathematics mixed with the reality of the Universe is how we often create what we call paradoxes. We try to make scenarios of measuring distances from exact nothing point locations to exact nothing point locations in a real Universe__ with such points imaginary, and all entities continually in motion. This is an absurdity. A point of nothing has no dimensions, and thus takes up no three dimensional space, and I say it also takes up no dimension of what people imagine to be time. With a Universe of total change of state, motion; there is no instant of zero time. An arrow shot through the air does not stop an infinite number of points, or instants along its trajectory! The arrow, in fact, is already moving while it is in the quiver and mounted to the bow, as well as when it is stuck in the target. The differences being only the directions, and rates of motion.
Since math is something that the Universe could exist without, and remain as normal as a normal universe might be; and since, before man there was not any math that we know of... I classify math as Fantasy. It is not a reality of the Universe.
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Page Relevant Quotes
"Mathematics is not a science__ it is not capable of proving or disproving the existence of real things." "This is not to say, however, that mathematical inventions do not correspond to real things. They do, in most, and possibly all cases." Bridges to Infinity, by Michael Guillen
"All measurement, whether it is concerned with distance or time or weight or electrical current or intelligence or beauty, is merely comparison with a standard." The Main Stream of Mathematics. Edna E. Kramer, Ph.D.
"We shall find in our processes of calculation we have to deal with small quantities of various degrees of smallness.
We shall have also to learn under what circumstances we may consider small quantities to be so minute that we may omit them from consideration. Everything depends upon relative minuteness. ...Hence we know that in all cases we are justified in neglecting the small quantities of the second__ or third (or higher)__ orders, if only we take the small quantity of the first order small enough in itself.
But it must be remembered that small quantities, if they occur in our expressions as factors multiplied by some other factor, may become important if the other factor is itself large." Calculus Made Easy, Silvanus P. Thompson, F.R.S.
"Why is the equivalence of the practically-rigid body and the body of geometry-which suggests itself so readily-denied by Poincare and other investigators? Simply because under closer inspection the real solid bodies in nature are not rigid, because their geometrical behaviour, that is, their possibilities of relative disposition, depend upon temperature, external forces, etc...
Sub specie aeterni Poincare, in my opinion, is right. The idea of the measuring-rod and the idea of the clock coordinated with it in the theory relativity do not find their exact correspondence in the real world." Sidelights On Relativity, Albert Einstein.
(Note: For Einstein... "Further, as to the objection that there are no really rigid bodies in nature... For it is not a difficult task to determine the physical state of a measuring-rod so accurately that its behaviour relatively to other measuring-bodies shall be sufficiently free from ambiguity to allow it to be substituted for the 'rigid' body.")
"Yet in the long run most physicists could not eschew visualization. They found that they needed imagery. A certain kind of pragmatic, working theorist valued a style of thinking based on a kind of seeing and feeling. That was what physical intuition meant. Feynman said to Dyson, and Dyson agreed, that when Einstein stopped creating it was because 'he stopped thinking in concrete physical images and became a manipulator of equations." Genius, The Life and Science of Richard Feynman, James Gleick
"A line drawn on a paper with a pencil or pen, of course, has some width and even a slight thickness.
Think of lines drawn with finer and finer pen points and then imagine a line that has no width or thickness whatsoever. Such a line we call a geometric line as distinguished from an actual line drawn on paper.
Do you think it is possible for any actual line to be absolutely straight? Suppose that you drew a line as straight as you possibly could with a sharp pencil and straight edge. If you could magnify it a thousand times its size, it would look as jagged as the edge of a saw. It is easy, however to imagine a geometric line to be straight. You have only to think what we mean by 'straight' and you are thinking of a geometric straight line. ...We shall continue to speak of 'drawing a line,' but we cannot, of course, draw a geometric line. ...Geometric point. We say that two straight lines intersect at a point (if not parallel). The intersection of two geometric lines has no dimensions whatever__ just position. Such a point we call a geometric point. Surface ...Similarly, a geometric surface may be thought of as a path of a moving geometrical line. For example, a vertical line moving along a horizontal line would form a plane surface, as the surface of a wall." Modern-School Geometry; John R. Clark, Rolland R. Smith.
"... the arbitrary hypotheses. The most important of these was that of Fitzgerald developed by Lorentz, and known as the Fitzgerald contraction hypothesis.
" According to this hypothesis, when a body is in motion it becomes shortened in the direction of motion by a certain proportion depending upon its velocity..."
" ...Later on, when Einstein propounded his special theory of relativity (1905), it was found that the hypothesis was in a certain sense correct, but only in a certain sense. That is to say, the supposed contraction is not physical fact, but a result of certain conventions of measurement..." The ABC of Relativity, Bertrand Russell.
"Part of the answer may be that to some extent we force our ideas on nature. A trajectory, after all is not perfectly parabolic, nor a planetary orbit perfectly elliptical. We choose to ignore the imperfections and concentrate on finding in nature what our minds have invented." Rainbow, Snowflakes, and Quarks; Hans C. von Baeyer.
